A method and a system for 3d imaging

ABSTRACT

A method for 3D surface imaging of an object, comprising generating a sinusoidal pattern from an input beam; projecting the sinusoidal pattern onto the object; acquiring deformed structured images from the object; reconstructing and displaying the surface of the object in real-time. A system comprises an device encoding an input beam with a structured pattern; a filter configured to spatially filter the encoded beam; a projector lens projecting the structured pattern onto the object; a high speed camera acquiring a structured pattern deformed by the 3D surface of the object; a graphic processing unit; and a CoaXPress interface transferring data acquired by the camera to the graphic processing unit; the graphic processing unit reconstructing and displaying the 3D surface of the object in real-time.

FIELD OF THE INVENTION

The present disclosure relates to 3D imaging. More specifically, thepresent disclosure is concerned with a method and a system for real-timehigh-speed three-dimensional surface imaging.

BACKGROUND OF THE INVENTION

Three-dimensional (3D) surface imaging is used in a range of fields,including machine vision [1], remote sensing [2], biomedical engineering[3], and entertainment [4]. Demands for higher spatial resolution, alarger field of view (FOV), and a higher imaging speed have generated anumber of 3D surface imaging methods [5-7].

Among them, structured-light profilometry (SLP) has become themainstream technique [8]. In a typical setup, a projector deliversstructured patterns onto an object. The structured patterns, deformed bythe 3D surface of the object, are captured by a camera. The 3Dinformation of the object is then extracted by analyzing the deformationof the patterns with respect to reference phase profiles. Among existingchoices of structured patterns in structured-light profilometry (SLP)[9], grayscale sinusoidal fringes are most widely used because theyprovide 3D data with both high spatial resolution and high depthaccuracy [10] as well as their suitability for high-speed 3Dmeasurements [11]. Digital micromirror devices (DMDs) are commonly usedto generate sinusoidal fringes. Each micromirror on a DMD can beindependently tilted to either+12° or −12° from its surface normal togenerate binary patterns at up to tens of kilohertz (kHz). Bycontrolling the overall reflectance via temporal dithering, the DMD canproduce grayscale sinusoidal patterns [12]. The DMD-basedstructured-light profilometry (SLP) is flexible in system developmentand accurate in 3D measurements [13-16].

Development of DMD-based SLP has allowed high-speed 3D surface imagingin real time, defined as image acquisition, processing, and displayduring the occurrence of dynamic events [17]. Nonetheless, most existingsystems still have limitation in terms of fringe pattern generation,image acquisition and processing. Micromirror-dithering clamps the speedof generating 8-bit grayscale images to around 100 Hz [18], whichexcludes 3D profilometry of a range of moving objects, such as beatinghearts and vibrating membranes [19, 20]. This limitation can bemitigated by using binary defocusing [21-23], which generates apseudo-sinusoidal pattern at an unconjugated plane to the DMDs byslightly defocusing the projector. However, this method compromises thedepth sensing range [24] and is less flexible when used with binarypatterns with different periods. Meanwhile, the uneven surface of theDMDs [25] may induce image distortion to the defocused sinusoidalpatterns at the unconjugated plane, which may decrease measurementaccuracy especially under coherent illumination.

Image acquisition devices and image processing modules in existing SLPsystems also have limitations. Most high-speed cameras deployed in SLP,despite having ultra-high imaging speeds, are not equipped with ahigh-speed interface to transfer data on time. This bottleneck alsohampers the on-line processing software developed based on graphicsprocessing units (GPUs) [26]. As a result, these systems cannotcontinuously stream data, further limiting their application scope tohighly synchronous events.

There is still a need in the art for a method and a system for real-timehigh-speed three-dimensional surface imaging.

SUMMARY OF THE INVENTION

More specifically, in accordance with the present invention, there isprovided a method for 3D surface imaging of an object, comprisinggenerating a sinusoidal pattern from an input beam; projecting thesinusoidal pattern onto the object; acquiring deformed structured imagesfrom the object; reconstructing and displaying the surface of the objectin real-time.

There is further provided a system for real-time high-speed 3D surfaceimaging of an object, comprising an device encoding an input beam with astructured pattern; a filter configured to spatially filter the encodedbeam; a projector lens projecting the structured pattern onto theobject; a high speed camera acquiring a structured pattern deformed bythe 3D surface of the object; a graphic processing unit; and a CoaXPressinterface transferring data acquired by the camera to the graphicprocessing unit; the graphic processing unit reconstructing anddisplaying the 3D surface of the object in real-time.

Other objects, advantages and features of the present invention willbecome more apparent upon reading of the following non-restrictivedescription of specific embodiments thereof, given by way of exampleonly with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In the appended drawings:

FIG. 1 is a schematic view of a bandwidth-limited 3D profilometry systemaccording to an embodiment of an aspect of the present disclosure;

FIG. 2 shows experimental results of a beam profiler test of the systemof FIG. 1; and

FIG. 3 shows an example of reconstruction results of static objectsusing the system of FIG. 1;

FIG. 4A is a schematic view of a system according to an embodiment of anaspect of the present disclosure;

FIG. 4B is a comparison of central cross sections of spectral powerdensity of a target sinusoidal pattern, a corresponding binary DMDpattern, and experimentally captured image;

FIG. 4C shows a grayscale sinusoidal pattern generated experimentally byband-limited illumination (top panel), and comparison of the averagedcross section of the pattern with a fitted result (bottom panel);

FIG. 5A is a schematical view of an experimental setup forquantification of the depth resolution of the system of FIG. 4A;

FIG. 5B shows a reconstructed image of planar surfaces of an object,dashed boxes representing selected regions for analysis;

FIG. 5C shows a measured depth difference between the planar surfaces ofFIG. 5B;

FIG. 6A shows reconstructed image of interlocking brick toys (left) anddepth profiles of selected centerlines (right) using the system of FIG.4A;

FIG. 6B shows reconstruction results of a bear toy with differentperspective angles and close-up views, scalar bar: 10 mm, using thesystem of FIG. 4A;

FIG. 6C shows reconstruction results of a lion toy and a horse toy withdifferent perspective angles and close-up views, scalar bar: 10 mm,using the system of FIG. 4A;

FIG. 7A shows a front view of reconstructed 3D images at 0 ms, 30 ms, 60ms and 90 ms of a rotating fan, using the system of FIG. 4A;

FIG. 7B shows a side view of the reconstructed 3D image of FIG. 7A at 60ms;

FIG. 7C shows depth line profiles along a radial direction over time;

FIG. 7D shows depth dynamics of selected points;

FIG. 8A shows reconstructed 3D images of a flapping flag at differenttimes;

FIG. 8B shows evolution of 3D positions of selected points of theflapping flag;

FIG. 8C shows phase relation of the y-z positions of the selected pointp_(c) and the fitted result;

FIG. 8D shows superimposed centerlines of the flag over time; the polebeing defined to zero in the z axis;

FIG. 9A shows the target fringe patterns;

FIG. 9B shows binary DMD patterns corresponding to the target fringepatterns of FIG. 9A, close-up views in the first panels show thegrayscale and binary characteristics of the target pattern and the DMDpattern, respectively;

FIG. 10 schematically shows geometry of point determination;

FIG. 11A shows four-step phase shifted illumination;

FIG. 11B shows an intensity profile of a selected pixel;

FIG. 12 is a flowchart of GPU-based real-time image processing;

FIG. 13A shows, in a system calibration, a captured image of thecheckerboard pattern, “0” representing the selected corner point; “X”and “Y” representing the 2D coordinates; dots representing the softwareextracted grid corners;

FIG. 13B shows camera calibration results with all the positions of thecheckerboard poses;

FIG. 13C shows images of a selected horizontal fringe pattern, thehorizontal centerline, a selected vertical fringe pattern, and thevertical centerline;

FIG. 13D is a camera image with selected grids;

FIG. 13E is a projector image with the corresponding grids;

FIG. 14A, in determination of minimal exposure time in depth resolutionquantification, shows a relation between measured depth differences andthe corresponding exposure times;

FIG. 14B shows 3D images of the planar surfaces and measured depthdifference at four exposure times;

FIG. 15A, in case of a real-time 3D imaging of a swinging pendulum at 1kHz, shows representative 3D images of the swinging pendulum at fivedifferent times; and

FIG. 15B shows depth traces of a selected point shown in FIG. 15A.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention is illustrated in further details by the followingnon-limiting examples.

In a system as illustrated in FIG. 1, a beam expander 20 is used toexpand a laser beam 12 to fully cover the active area of an encodingdevice 18, so that the laser beam can make full use of the completelyactive area of the encoding device 18. Mirrors M1, M2 direct theextended laser beam to the encoding device 18 with a specific angle.After encoding by the encoding device 18, the beam profile is spatiallyfiltered in a 4 f system (lenses L3, L4) and a pinhole 22 positioned atthe Fourier plane. A projector lens 24 at the image plane of the 4 fsystem projects the pattern onto the object 26. A high-speed camera 14is used in conjunction with a frame grabber (not shown) for acquiringthe structured patterns deformed by the 3D surface of the object 26.

The illumination source is a continuous-wave laser 12 with an outputpower of at least 200 mW, and a wavelength selected according to thecamera's response, in a range between 420 and 700 nm. The beam expander20 has a magnification time of more than 8, a maximum input beamdiameter of more than 1.2 mm, and a wavelength range selected to coverthe illumination wavelength. The mirrors M1 and M2, with a diameter ofat least 2″, have a wavelength range selected to cover the illuminationwavelength.

The encoding device 18 is a spatial light modulator such as a digitalmicromirror device (DMD), with a resolution of more than 1 Mega pixelsand a full frame refreshing rate: of at least 5 kHz.

The two double-convex lens L3, L4, of a diameter of at least 2″ andfocal length between 100 and 200 mm, have a wavelength range selected tocover the illumination wavelength. Optical low-pass filtering isachieved by a pinhole 22 of a diameter higher than 125 μm.

The projector lens 24 has focal length between 18 and 55 mm, and amaximum aperture off/3.5-5.6. The high-speed camera 14 has a frame rateof at least 5k frames/second, and more than 250 k pixels on the sensor.

A beam profiler 16 at the image plane of the 4 f system is used to testthe projected pattern P1. From experimental data, curve-fitting tools aeused to compare the projected binary pattern P1 and a target profile P2defined as a sinusoidal intensity constrained by a Gaussian envelope(Gaussian function×sine function). The fitting results are as shown inFIG. 2.

After testing the projected pattern P1, the system and method wereapplied to a 3D reconstruction experiment with static target objects.The camera resolution was set to be 1280×860 pixels. The four-step phaseshift method was used to extract the phase value (λ=80 pixels). 3D pointcloud reconstruction of static toy animals in FIG. 3 shows high qualityof detailed information recovery.

The system and method is thus shown to allow grayscale sinusoidalpattern formation from a single static programmed binary pattern by ahigh-precision laser beam shaping system based on a DMD. An errordiffusion algorithm may be applied in the binary pattern generation. Themethod may be used to project sinusoidal patterns on the image planewithout mirror dithering.

The bandwidth limited projection is used in structural illumination. Itenables sinusoidal pattern generation using a single binary patternloaded onto the DMD. In addition, the sinusoidal pattern is formed at afixed image plane, regardless of the spatial period of the sinusoidalpatterns. In this regard, the present method solves previous problems inbinary defocusing method. In addition, by leveraging the high refreshingrate of the DMD, the present method has the ability to projectsinusoidal patterns at a speed of several thousand frames per second,which enables kilohertz-level 3D profilometry.

The present system and method of FIGS. 1-3 provide a fast 3Dprofilometer. In addition, such system and method have applications insuper-resolution microscopy. Moreover, they may provide a cost-effectivealternative in the field of passive ultra-high-speed imaging.

In a system according to another embodiment of an aspect of the presentdisclosure illustrated in FIG. 4A for example, a continuous-wave laser(671-nm wavelength and 200-mW power, such as MRL-III-671, CNI Lasers forexample) is used as the light source 12. After expansion and collimationby lenses L1 and L2, the laser beam is directed to a 0.45″ DMD 18 at anincident angle of about 24° with respect of its surface normal. Binarypatterns loaded onto the DMD 18 generate sinusoidal fringes at theintermediate image plane (IIP) by the band-limited 4 f imaging system(lenses L3 and L4; pinhole 22).

The projector lens 24 projects these fringes onto the 3D object 26 witha field of view (FOV) of 100 mm×100 mm. The deformed structured imagesscattered from the object 26 are captured by a high-speed CMOS camera 14at 5 kHz with 512×512 pixels in each frame. The captured images aretransferred to a host computer 30 with via a CoaXPress interface 32connected to a frame grabber (such as Cyton-CXP, Bitflow for example). AGPU-based image processing software is used for 3D image reconstructionin real-time.

The CoaXPress interface 32, with a data transfer speed of at least 25Gbps for example, is used for high-speed data acquisition. The GPU, witha memory speed of a least 8 Gbps, memory bandwidth of a least 192GB/sec, NVIDIA CUDA® Cores of a least 1152 for example, allows real-timedata processing.

In a method for real-time, high-speed 3D surface imaging in aCoaXPress-interfaced band-limited illumination profilometry (CI-BLIP)according to an embodiment of an aspect of the present disclosure,band-limited illumination is thus used to generate and projecthigh-quality sinusoidal fringe patterns at 5 kHz. The set of targetimages contains four grayscale sinusoidal fringe patterns (648-μmperiod) with phase shifts from 0 to 3π/2 with a step of π/2 as well asone vertical stripe pattern. Each individual grayscale fringe pattern isfirst converted to its corresponding binary DMD pattern using anadaptive error diffusion algorithm [27] as described in Supplementarysection Note 1 hereinbelow and FIGS. 9. The generated binary DMDpatterns have blue noise characteristics in the spatial frequencydomain, which manifest by imaging content precisely matched to thecorresponding grayscale pattern within the bandwidth of the system (FIG.4B). The 150-μm pinhole 22 placed at the Fourier plane in the 4 fimaging system is used to filter high-spatial-frequency noise. Theresultant beam profile shows high-quality grayscale sinusoidal fringes(FIG. 4C), with a root-mean-square error of 4.18% with respect to thetarget pattern. The band-limited illumination method is thus shown togenerate accurate sinusoidal patterns at the conjugate plane of the DMD,which avoids the depth-dependent blurring effect and image distortion,thus improving the operating flexibility method compared with binarydefocusing methods.

Moreover, combining a CoaXPress-interfaced high-speed camera with aGPU-based software provides a synergy between the high-speed camerainterface and the GPU-based processing that allows real-time high-speed3D image reconstruction. The CXP cable 32, with a bandwidth of 25 Gbps,enables continuous streaming of fringe images to the host computer 30during image acquisition at 5 kHz. These images are stored into RAM viadirect memory access operations independent from the CPU. Afterdetermining the vertical stripe pattern, the calibration frame and fourfringe patterns in GPU are processed, beginning with the parallelizedextraction of wrapped phase and quality map information (seeSupplementary section Notes 2-5 and FIG. 10 hereinbelow). Phaseunwrapping is then carried out via the GPU accelerated implementation ofa two-dimensional (2D) weighted phase unwrapping algorithm [28, 29],which uses the quality map information to guide the unwrapping procedureagainst errors induced by noise. The selected algorithm relies on theindependent manipulation of points using 2D discrete cosinetransformation [30]. Absolute phase is then computed in parallel byadding a constant determined from the vertical stripe pattern. Finally,coordinate information is recovered from the absolute phase map fromeach pixel via matrix inversion., enabling real-time 3D positiontracking at 1 kHz. Thus, continuous streaming of fringe images to thehost computer during image acquisition at 5 kHz with a bandwidth of 25Gbps and a real-time three-dimensional position tracking at 1 kHz isachieved.

To quantify the depth resolution of the CoaXPress-interfacedband-limited illumination profilometry of the present disclosure, twostacked planar surfaces offset by about 5° were imaged (FIG. 5A). Inthis configuration, the depth difference between the two surfaces alongthe x axis increased monotonously, starting from negative maximum at theright edge, to zero at the center, and reaching positive maximum at theleft edge. The reconstructed image of the 3D object (FIG. 5B) allowedanalyzing cross sections of depth at different×positions (see FIG. 14Aand Supplementary Note 6 hereinbelow). The depth difference (denoted byΔz) of the two surfaces, which closely agrees to the ground truth, wascalculated (FIG. 5C). In addition, standard deviations of the measureddepths were used as the noise level of the system. The depth resolutionwas defined as when Δz is two times the noise level of the system. Thedepth resolution of CoaXPress-interfaced band-limited illuminationprofilometry (CI-BLIP) was 0.15 mm.

Various static 3D objects were imaged to assess the feasibility ofCoaXPress-interfaced band-limited illumination profilometry (CI-BLIP).First, three interlocking brick toys, with studs of respective heightsof 23 mm, 15 mm, and 3 mm, were measured. Reconstructed results andselected centerlines are plotted in FIG. 6A, showing that the structureinformation of the brick toys is accurately recovered, allowing forexample identification of shallow dents of a depth of about 1 mm at thecenters of the studs (see arrows in FIG. 6A). Experiments conducted onsingle and multiple animal toys (FIGS. 6B-6C). The depth information isshown in two perspective images and the detailed surface structures areillustrated by close-up views.

To assess real-time high-speed 3D surface profilometry,CoaXPress-interfaced band-limited illumination profilometry (CI-BLIP)was used to image an electric fan rotating at 300 rounds per minute. Thefan has seven blades, each having a tilt angle of bout 30°. FIG. 7Ashows the front view of reconstructed 3D images at four time points andFIG. 7B shows a representative side view (FIG. 7B). Detailed 3D shapesof the base, center hub, side cover, blades, and bars underneath theblades can be identified, showing that the present method allowstracking the evolution of depth over the entire FOV. As an example, FIG.7C shows line profiles along the radial direction (marked by the solidline in the first panel of FIG. 7A) over time. The blade quickly sweptthrough the radical profile in 14 ms, resulting in a maximum change indepth of 6 mm. To further analyze details in depth dynamics, FIG. 7Dshows the depth profiles of three points, including one point on thecentral hub (p_(A)) and two points along a blade (p_(B) and p_(C),). Thedepth profiles of p_(A) to p_(C) clearly illustrate the linearrelationship between the displacements of the fan blades with differentradii at a constant angular speed of about 30 rad/s. The depth of p_(A)does not show apparent change, which is in accord with the flat centralhub. The periodic displacements in depth of p_(B) and p_(C) show thatthe fan had a rotation period of approximately 210 ms. These measuredresults are in agreement with preset experimental conditions. Selectedresults from the 1-kHz real-time reconstruction of this scene weredisplayed at 60 Hz and also showed real-time 1-kHz tracking of the 3Dposition of a selected single point.

The method and system were further used to image flapping dynamics of aflag with a maple leaf pattern (80 mm×50 mm in size) mounted on a poleand exposed to a strong wind produced by an air blower. FIG. 8A showsrepresentative 3D images of instantaneous poses of the flapping flagfrom two perspective views, showing a wave travelling toward the edge atapproximately 2 m/s. Time histories of the streamwise (x axis), spanwise(y axis), and transverse (z axis) displacements of three selected pointsmarked as p_(A), p_(B), and p_(C), with p_(A) at the mid-point in the yaxis; p_(B) and p_(C) having the same x coordinate are shown (FIG. 8B).The displacements of p_(A) have the smallest amplitudes in all threedirections, representative of a less intense flapping motion in the partof the flag closer to the pole. The streamwise and transversedisplacements of p_(B) and p_(C) show an apparent phase difference,which is attributed to a gravity-induced sagging effect. The phaserelation between the spanwise and transverse displacements of p_(C)(FIG. 8C) exhibits an elliptical shape in both experimental and fittedresults, showing that the flapping motion is dominated bysingle-frequency sinusoidal waves. Finally, the depth curves of themiddle line of the flag in all reconstructed images (FIG. 8D) shows anasymmetric flapping motion toward the +z direction, which indicatesuneven forces submitted to the flag surface and a relatively high degreeof turbulent flow.

A CoaXPress-interfaced band-limited illumination profilometry (CI-BLIP)according to an embodiment of an aspect of the present disclosurecomprises generating a binary pattern, in which a grayscale sinusoidalpattern is processed by an adaptive error diffusion algorithm into acorresponding binary pattern able to be displayed on the DMD with upperlimit speed (step 110). Band-limited illumination of the object thenmakes use of a 4 f imaging system with a pinhole on the Fourier plane tofilter high-spatial frequency noise, as well as a projector lens toproject the pattern displayed on the DMD; each binary pattern displayedon the DMD is projected to be a grayscale sinusoidal image with highquality (step 120). A calibration step may comprise imaging acheckerboard with multiple different positions and calculating thespatial relationship by a calibration toolbox in MATLAB, so as todetermine the extrinsic and intrinsic parameters of the pinhole modelsof camera and projector (step 230). In a data acquisition step (step140), a CoaXPress interface is used between the camera and the hostcomputer to continuously stream data at 25 Gbps, for acquisition ofimages carried with objects structural information are acquired andtransferred to GPU. In a reconstruction step (step 150), the absolutephase value is calculated by GPU parallel processing and transferredinto spatial information with calibration data. The 3D information(x,y,z) of the object's surface is extracted from each full-sequence(five images) of structured pattern illumination. The solved depthvalues are linearly mapped to an 8-bit range suitable for real-timedisplay, the dynamic of objects in 3D being displayed at 60 Hz (fullframe), with single point depth tracking at 1 kHz.

There is thus provided a CoaXPress-interfaced band-limited illuminationprofilometry (CI-BLIP) method that integrates band-limited illumination,CoaXPress-interfaced high-speed image acquisition, and GPU-based imagereconstruction. The present high-speed structured-light profilometry(SLP) system and method allow real-time 3D position tracking at 1 kHz,which may be further improved by using a high-power laser, a fastercamera interface [32], and advanced phase unwrapping algorithms [33].

The present method and system may be used in a range of applications,including in-situ industrial inspection, dynamic biometric analysis, andvibration measurement for acoustics.

They may be combined with studies of fluid-structure interactions. Themechanisms that govern the flag-wind interaction has generatedscientific interests in diverse studies [37], including animal ethology[38], paper engineering [39], and hydroelectric power generation [40].Due to its complex geometries and freely moving boundaries [31], studythe gravity-induced impact in flag-fluid interaction remains achallenge. Thus far, although many simulation works have been carriedout to investigate the relation between gravity and the stability offlags with different flow air conditions [41-43], experimentalvisualization of real-time flag movement is still a challenge. A limitednumber of experiments were conducted using low flow speeds [44, 45] andrigid flags, which restricted the analysis of fluid dynamics in 2D.

In contrast, the present CoaXPress-interfaced band-limited illuminationprofilometry (CI-BLIP) system and method allow 3D analysis of atravelling wave, the gravity-induced phase mismatch, and the asymmetricfluctuation of a non-rigid flapping flag at 1 kHz. The ability of thepresent CoaXPress-interfaced band-limited illumination profilometry(CI-BLIP) system and method for continuous streaming acquired data mayalso contribute to imaging unpredicted or non-repeatable flow dynamics.

Supplementary Section Note 1: Design of Band-Limited Illumination

Design of binary patterns: The gradient-based adaptive error diffusion(GAED) algorithm [27], a halftoning technique, was used to design thebinary patterns that were loaded onto the digital micromirror device(DMD). In the experiment, four grayscale sinusoidal patterns, with aperiod of 60 digital micromirror device (DMD) pixels and with phaseshifts of 0,

$\frac{\pi}{2},\pi,{{and}\frac{3\pi}{2}}$

(Supplementary FIG. 1 left column) were used as the input images. Eachgrayscale pattern was processed by the GAED algorithm to produce onebinary digital micromirror device (DMD) pattern pixel by pixel from leftto right in a row and then from top to bottom row by row. For a specificdigital micromirror device (DMD) pixel, its binary value was determinedby a dynamic threshold that depended on the gradient magnitude of thecurrent pixel in the grayscale image [27]. Then, the binarization errorof the processed pixel in the grayscale image was diffused to theneighboring pixels based on specific weights, which resulted in theintensity change of the surrounding pixels accordingly. By rasterprocessing, the binary digital micromirror device (DMD) pattern wasobtained (FIG. 9B).

Determination of the bandwidth of the system: The bandwidth of thesystem is controlled by a pinhole as a low-pass filter. The diameter ofthe pinhole, D, is calculated by

$\begin{matrix}{{D = \frac{\lambda f_{3}}{P_{f}}},} & ({S1})\end{matrix}$

where P_(f)=648 μm denotes the fringe period (which equals to 60 digitalmicromirror device (DMD) pixels), λ=671 nm is the laser wavelength,f₃=120 mm is the focal length of L3. Thus, the required pinhole diametersize is D=124.26 μm. In the experiment, a 150-μm pinhole was used in thesimulation to conduct optical low-pass filtering. The correspondingnormalized system bandwidth is 0.01. It is worth noting that the actualpinhole size is slightly larger than the calculated value so that allspatial frequency content of the sinusoidal fringe pattern areguaranteed to pass through it

Note 2: Geometry of Point Determination in 3D Space

The geometrical configuration of the method, following that ofconventional structured-light profilometry, is shown in FIG. 9, whichshow the target fringe patterns (FIG. 9A) and their corresponding binaryDMD patterns (FIG. 9B). Close-up views in the first panels show thegrayscale and binary characteristics of the target pattern (FIG. 9A) andthe DMD pattern (FIG. 9B)., respectively Adopting the usual pinholemodel, a selected camera pixel (x, y) and the center point of the cameradetermine a line that emerges from the camera into space. The 3Dcoordinates of an object point viewed from the pixel, althoughconstrained to this line, are indeterminate because of the usual loss ofdepth information in 2D images. The projector, modeled as a “reverse”pinhole camera, serves to recover this information by encoding pointsalong this line within a deterministic sequence of structured lightpatterns. After a sequence of such projections is recorded by thecamera, 3D coordinates can be recovered by examining the intensitysequence reported by each camera pixel. Despite a vast and still-growingnumber of general patterning schemes [18], it is sufficient to deploypatterns that encode only the columns of the display surface of theprojector. Thus, FIG. 10 considers the case in which the intensitysequence of a (x, y) pixel decodes to a corresponding column x_(p) ofthe DMD. This column and the center point of the projector determine aplane whose intersection with the projected camera ray determines therecovered 3D point.

Mathematically, the relationship between a 3D point P=[X Y Z]^(T) andits locations on the 2D camera sensor (x, y) and DMD (x_(p), y_(p)) aredescribed as

$\begin{matrix}{{{s\begin{bmatrix}x \\y \\1\end{bmatrix}} = {{A\left\lbrack {R,T} \right\rbrack}\begin{bmatrix}P \\1\end{bmatrix}}},{{{and}{s_{P}\begin{bmatrix}x_{P} \\y_{P} \\1\end{bmatrix}}} = {{A_{P}\left\lbrack {R_{P},t_{P}} \right\rbrack}\begin{bmatrix}P \\1\end{bmatrix}}},} & ({S2})\end{matrix}$

where [x y 1]^(T) and [x_(p) y_(p) 1]^(T) are the homogenous coordinatesof the camera pixel and the DMD pixel respectively, {R, R_(p)} are 3×3rotation matrices, {T, T_(p)} are 3×1 translation vectors, [P 1]^(T)=[XY Z 1]^(T) are the homogenous coordinates of P, and {s, s_(p)} arearbitrary scaling factors. The matrices [R, T] and [R_(p), T_(p)]describe the “extrinsic” properties of the camera and projector bydefining their positions and orientations relative to the worldcoordinate system. On the other hand, the 3×3 matrices {A, A_(p)}describe the “intrinsic” image forming properties of the pinholecamera/projector, and each takes the form:

$\begin{matrix}{\begin{bmatrix}f_{x} & \alpha & x_{0} \\0 & f_{y} & y_{0} \\0 & 0 & 1\end{bmatrix},} & ({S3})\end{matrix}$

where {f_(x), f_(y)} describe separate horizontal and vertical focallengths, (x₀, y₀)identify the coordinates of the principal point of theimage plane, and a accounts for (possible) pixel skewness. Together, {A,R, T} form a set of calibration parameters that must be estimatedseparately for both the camera and projector. With knowledge of thecalibration parameters, and once (x, y) and x_(p) are determined,Equation (S2) can be rearranged into a single matrix equation of theform [x y x_(p)]T=M P, from which the 3D point P is recovered via matrixinversion.

Supplementary Note 3: Phase Shifting and Unwrapping

In phase shifting profilometry, 3D measurement begins with the captureof N fringe images of the 3D scene under illumination from N fringepatterns. Because of equal fringe shifting, a pixel at camera coordinate(x, y) will report a sinusoidally varying intensity across the acquiredimages. This intensity response can be considered as

I _(k)(x,y)=I′(x,y)+I″(x,y)cos [φ(x,y)−2πk/N],  (S4)

Here I_(k)(x, y) represents the camera recorded intensity from the pixelat coordinates(x, y) in the k^(th) image. I′(x, y) and I″(x, y)represent the average pixel intensity and intensity modulation depth dueto fringe projection, φ(x, y) represents a phase offset, and k=0,1, . .. N−1. In particular, φ(x, y), encoded by the corresponding location ofthe pixel within the field of view of the projector, enables 3Dreconstruction. Across all image pixels, the three parameters φ(x, y),I′(x, y), and I″(x, y) can be found as

$\begin{matrix}{{{\varphi\left( {x,y} \right)} = {\tan^{- 1}\left( \frac{\sum_{k = 0}^{N - 1}{{I_{k}\left( {x,y} \right)}\sin\left( \frac{2\pi k}{N} \right)}}{\sum_{k = 0}^{N - 1}{{I_{k}\left( {x,y} \right)}\cos\left( \frac{2\pi k}{N} \right)}} \right)}},} & ({S5})\end{matrix}$ $\begin{matrix}{{{I^{\prime}\left( {x,y} \right)} = {\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{I_{k}\left( {x,y} \right)}}}},{and}} & ({S6})\end{matrix}$ $\begin{matrix}{{I^{''}\left( {x,y} \right)} = {\frac{2}{N}{\begin{pmatrix}{\left\lbrack {\sum\limits_{k = 0}^{N - 1}{{I_{k}\left( {x,y} \right)}\sin\left( \frac{2\pi k}{N} \right)}} \right\rbrack^{2} +} \\\left\lbrack {\sum\limits_{k = 0}^{N - 1}{{I_{k}\left( {x,y} \right)}\cos\left( \frac{2\pi k}{N} \right)}} \right\rbrack^{2}\end{pmatrix}.}}} & ({S7})\end{matrix}$

Since values of φ(x,y) are fundamentally determined only up to multiplesof 2π, Equation (S5) provides wrapped values in the interval (−π, π].Importantly, since Equations (S5)-(S7) solve for three parameters, it isgenerally required that N≥3. In the present work, N=4 (see FIG. 11) wasused, for which the form of Equation (S5) becomes

${\varphi\left( {x,y} \right)} = {{\tan^{- 1}\left( \frac{I_{1} - I_{3}}{I_{0} - I_{2}} \right)}.}$

To perform 3D reconstruction on objects, it is necessary to unwrap andpossibly offset the values of φ(x,y) to obtain an absolute phase thatcan be converted to the coordinates of a pixel within the field of viewof the projector. The weighted discrete cosine transform based phaseunwrapping procedure [29, 28] was used. For this phase unwrappingprocedure, the modulation values I″(x,y) were used to produce qualitymaps to guide unwrapping. To obtain absolute phase, a single verticalfringe was used as an additional pattern. Thresholding the values inthis additional image allowed for a subset of the unwrapped phase map tobe associated with the center of the DMD projector. Absolute phase wasthen obtained relative to the center of the DMD by averaging unwrappedphase values over the subset to obtain a phase offset value φ₀ that wassubtracted from the unwrapped phase. Horizontal projector coordinatesx_(p) (x, y) were then obtained as a linear function of the absolutephase by:

$\begin{matrix}{{{x_{p}\left( {x,y} \right)} = {{\left( {{\overset{˜}{\varphi}\left( {x,y} \right)} - \varphi_{0}} \right)\frac{P_{p}}{2\pi}} + {\frac{1}{2}\left( {N_{x} - 1} \right)}}},} & ({S8})\end{matrix}$

where {tilde over (φ)}(x, y) is the unwrapped phase, P_(p) is the fringeperiod (in pixels), and N_(x) is the width of the DMD (in pixels).

Supplementary Note 4: Real-Time Image Processing

Displayed in FIG. 12, first, a set of five consecutively recorded framesare distinguished into an ordered group of four frames containing fringecontent and a single frame containing the DMD calibration fringe. Then,wrapped phase and quality map data are extracted according to the fringeshifting algorithm. Phase unwrapping determines unwrapped phase map.Absolute phase is determined using data from the calibration frame. Inaddition, pixel coordinate data are solved in parallel using Cramer'srule [48]. Finally, depth values are linearly mapped to produce a bitmapsuitable for direct display.

Supplementary Note 5: System Calibration

Camera calibration: The calibration of camera was conducted to extractthe intrinsic parameters of the camera model. A 9×11 black/whitecheckerboard pattern was used, on which each square was 8 mm×8 mm insize (FIG. 13A). 20 poses of this checkerboard were imaged (FIG. 13B). AMATLAB toolbox [49] was used to extract the grid corners and calculatethe camera's intrinsic parameters of the focal length, the principlepoint, pixel skewness, and distortion.

Projector calibration: In the calibration of projector, the key conceptis to enable the projector to “capture” images like a camera, thusmaking the calibration the same as that of a camera. The method [50]involved capturing additional images of the checkerboard pattern underillumination of both horizontally and vertically shifted fringe patterns(FIG. 13C). Estimation of the absolute phase from these images wascarried out using the four-step phase shifted algorithm as described inSupplementary Note 3. Then, the absolute phase maps extracted for boththe horizontal and vertical directions were used to determine apixel-wise mapping between camera-captured images of the checkerboardplane (FIG. 13D) into correctly altered images representing the view ofthe checkerboard plane from the perspective of the projector (FIG. 13E).Finally, the MATLAB toolbox was used to compute the calibrationparameters of the projector, including the principal point, the focallength, and skewness.

Supplementary Note 6: Additional Information of Depth ResolutionQuantification

FIG. 14 show the experimental results of depth resolution quantificationwith different exposure times. The reconstruction results deterioratewith short exposure times (FIG. 14A) In particular, at the exposure timeof 150 μs, the limited number of scattered photons received by thecamera resulted in an unsuccessful reconstruction in a small area on theleft. However, the rest of the planar surfaces could still be recovered.At the exposure time of 50 μs, the region of unsuccessful reconstructionprevailed across the entire planar surfaces. Further analysis (FIG. 14B)shows that that the noise dominates the calculated depth difference.Therefore, the minimal exposure time was determined to be 150 μs.

Supplementary Note 7: Additional Information of Real-Time kHz 3D Imagingof Dynamic Objects

FIG. 15 shows another dataset of high-speed 3D surface imaging of aswinging pendulum using CI-BLIP. Five representative 3D images of thependulum at different times are shown in FIG. 15A. The depth evolutionof a selected point on the pendulum was also tracked over time, which ismarked as Pin FIG. 14A. This result was filtered by using

$\begin{matrix}{{z = {{A{\sin\left\lbrack {\frac{2\pi}{T}\left( {t - t_{0}} \right)} \right\rbrack}} + B}},} & ({S9})\end{matrix}$

where A=42, T=400, t₀=100,B=241. As illustrated in FIG. 15B, thesinusoidal displacements of the selected point shows a period of ˜400ms. The length of the pendulum was measured to be L=˜40 mm, thetheoretical swinging period can be calculated as

$\begin{matrix}{{T_{theroy} = {2\pi\sqrt{\frac{L}{g}}}},} & ({S10})\end{matrix}$

where g=9.80665 m/s². T_(theroy) was calculated to be 401.4 ms, whichclosely agrees to the experimental result.

The scope of the claims should not be limited by the embodiments setforth in the examples but should be given the broadest interpretationconsistent with the description as a whole.

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1. A method for 3D surface imaging of an object, comprising generating asinusoidal pattern from an input beam; projecting the sinusoidal patternonto the object; acquiring deformed structured images from the object;reconstructing and displaying the surface of the object in real-time. 2.The method of claim 1, wherein said generating the sinusoidal patterncomprises encoding an input beam with a structured pattern.
 3. Themethod of claim 1, wherein said generating the sinusoidal patterncomprises encoding an input beam with a structured pattern and spatiallyfiltering high-spatial frequency noise from a resulting encoded beam. 4.The method of claim 1, wherein said generating the sinusoidal patterncomprises encoding an input beam with a structured pattern and spatiallyfiltering high-spatial frequency noise from a resulting encoded beamusing a 4f imaging system with a pinhole at the Fourier plane.
 5. Themethod of claim 1, wherein said generating the sinusoidal patterncomprises encoding an input beam with a structured pattern and spatiallyfiltering high-spatial frequency noise from a resulting encoded beamusing a 4f imaging system with a pinhole at the Fourier plane; saidprojecting the sinusoidal pattern comprising projecting the encoded beamonto the object using a projector lens positioned at the image plane ofthe 4 f system.
 6. The method of claim 1, wherein said acquiringdeformed structured images comprises using a high speed camera in aCoaXPress-interface with a computer.
 7. The method of claim 1, whereinsaid acquiring deformed structured images and said reconstructing anddisplaying the surface of the object in real-time comprises interfacinga high speed camera and a GPU with a CXP cable.
 8. The method of claim1, wherein comprising a continuous-wave laser with an output power of atleast 200 mW and a wavelength selected in a range between 420 and 700 nmas a source of the input beam.
 9. The method of claim 1, wherein saidgenerating the sinusoidal pattern comprises encoding the input beam witha structured pattern using a spatial light modulator with a resolutionof more than 1 Mega pixels and a full frame refreshing rate of at least5 kHz.
 10. The method of claim 1, wherein said generating the sinusoidalpattern comprises encoding the input beam with a structured patternusing a spatial light modulator with a resolution of more than 1 Megapixels and a full frame refreshing rate of at least 5 kHz, the methodcomprising expanding the input beam in relation to an active area of thespatial light modulator.
 11. The method of claim 1, wherein saidgenerating the sinusoidal pattern comprises encoding the input beam witha structured pattern using a spatial light modulator with a resolutionof more than 1 Mega pixels and a full frame refreshing rate of at least5 kHz, the method comprising expanding the input beam in relation to anactive area of the spatial light modulator using a beam expanderselected having a magnification time of more than 8, a maximum inputbeam diameter of more than 1.2 mm, and a wavelength range selected in arange between 420 and 700 nm.
 12. The method of claim 1, comprisingselecting a high speed camera of a frame rate of at least 5kframes/second, and a sensor with more than 250 k pixels.
 13. The methodof claim 1, comprising selecting a CoaXPress interface having a datatransfer speed of at least 25 Gbps, said GPU having a memory speed of aleast 8 Gbps, a memory bandwidth of a least 192 GB/sec, and NVIDIA CUDA®Cores of a least
 1152. 14. A system for real-time high-speed 3D surfaceimaging of an object, comprising: an encoding device; encoding an inputbeam with a structured pattern; a filter configured to spatially filterthe encoded beam; a projector lens projecting the structured patternonto the object; a high speed camera acquiring a structured patterndeformed by the 3D surface of the object; a graphic processing unit; anda CoaXPress interface transferring data acquired by the camera to thegraphic processing unit; the graphic processing unit reconstructing anddisplaying the 3D surface of the object in real-time.
 15. The system ofclaim 14, wherein said filter configured to spatially filter the encodedbeam comprises a 4 f system and pinhole positioned at the Fourier plane,and said projector lens is positioned at the image plane of the 4 fsystem.
 16. The system of claim 14, wherein a source of the input beamis a continuous-wave laser with an output power of at least 200 mW and awavelength selected in a range between 420 and 700 nm.
 17. The system ofclaim 14, wherein the encoding device is a spatial light modulator witha resolution of more than 1 Mega pixels and a full frame refreshing rateof at least 5 kHz.
 18. The system of claim 14, wherein the high speedcamera has a frame rate of at least 5k frames/second, and a sensor withmore than 250 k pixels.
 19. The system of claim 14, comprising a beamexpander selected with a magnification time of more than 8, a maximuminput beam diameter of more than 1.2 mm, and a wavelength range selectedin a range between 420 and 700 nm, said beam expander expanding theinput beam in relation to an active area of the encoding device.
 20. Thesystem of claim 14, said CoaXPress interface having a data transferspeed of at least 25 Gbps, said GPU having a memory speed of a least 8Gbps, a memory bandwidth of a least 192 GB/sec, and NVIDIA CUDA® Cores.